Data quality, concepts and methodology: Methodology

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For the first time, the Demographic Estimates Section releases simultaneously total estimates and estimates by age and sex. This should become a new practice intended to facilitate the use of our estimates. It may differ for the release of the intercensal estimates.

Please find enclosed postcensal quarterly demographic estimates for July 1, 2010. This document describes the concepts, data sources and methodology used to produce the population estimates. Population estimates are produced to measure the population counts according to various characteristics and geographies between two censuses. Population estimates are the official figures used for the count of the population at the national, provincial and territorial levels.

Population Estimates

Estimates of the total population

Types of estimates

Population estimates can be either intercensal or postcensal. Intercensal estimates are produced using counts from two consecutive censuses adjusted for census net undercoverage (CNU) ¹  (including adjustment for incompletely enumerated Indian reserves) and postcensal estimates. The production of intercensal estimates involves updating the postcensal estimates using the counts from a new census adjusted for CNU¹.

Postcensal estimates are produced using data from the most recent census adjusted for CNU¹ and the components of population growth. In terms of timeliness, postcensal estimates are more up-to-date than data from the most recent census adjusted for CNU¹, but as they get farther from the date of that census, they become more variable.

Levels of estimates

Updating population estimates between censuses entails the use of data from administrative files or surveys. The quality of population estimates therefore depends on the availability of a number of administrative data files that are provided to Statistics Canada by Canadian and foreign government departments. Since some components are not available until several months after the reference date, three kinds of postcensal estimates are produced preliminary postcensal (PP), updated postcensal (PR) and final postcensal (PD). The time lag between the reference date and the release date is three to four months for preliminary estimates and two to three years for final estimates. Though it requires more vigilance on the part of users, the production of three successive series of postcensal estimates is the strategy that best satisfies the need for both timeliness and accuracy of the estimates. All tables in the CD-ROM indicate the level of the estimates they contain.

Calculation of postcensal population estimates

Population estimates – preliminary, updated and final – are produced by the component method. This method consists in taking the population figures from the most recent census, adjusted for census net undercoverage (CNU¹) (census undercoverage minus census overcoverage), and adding or subtracting the number of births, deaths, and components of international and interprovincial migration.

A. Provincial / territorial estimates of total population

Population estimates are produced for the provinces and territories first; then they are summed to obtain an estimate of the population of Canada.

The component-method formula for estimating total provincial / territorial populations is as follows:

Figure 1

B. Provincial / territorial estimates by age and sex

Postcensal population estimates by age and sex are produced applying the component method to each age-sex cohort in the base population.

At age 0:

Figure 2

From 1 to 99 years:

Figure 3

For 100 years and over:

Figure 4

Figure 5

C. Levels of estimates

The difference between preliminary ²  and final postcensal population estimates lies in the timeliness of the components. When all the components are preliminary, the estimate is described as preliminary postcensal (PP). When they are all final, the estimate is referred to as final postcensal (PD). Any other combination of levels is referred to as updated postcensal (PR).

Base population and components of population growth

A. Base population

The base populations are derived from the quinquennial censuses between 1971 and 2006. The population universe of the 2006 ³  Census includes the following groups:

1. Canadian citizens (by birth or by naturalization) and landed immigrants with a usual place of residence in Canada;
2. Canadian citizens (by birth or by naturalization) and landed immigrants who are abroad, either on a military base or attached to a diplomatic mission;
3. Canadian citizens (by birth or by naturalization) and landed immigrants at sea or in port aboard merchant vessels under Canadian registry;
4. persons with a usual place of residence in Canada who are claiming refugee status and members of their families living with them;
5. persons with a usual place of residence in Canada who hold Study Permits and members of their families living with them;
6. persons with a usual place of residence in Canada who hold Work Permits and members of their families living with them.

For census purposes, the last three groups in this list are referred to as non-permanent residents (NPR).

Foreign residents have not been enumerated since 1991. Foreign residents are persons who belong to the following groups:

1. Government representatives of another country attached to the embassy, high commission or other diplomatic body of that country in Canada, and members of their families living with them;
2. members of the Armed Forces of another country who are stationed in Canada, and members of their families living with them;
3. residents of another country visiting Canada temporarily (for example, a foreign visitor on vacation or on business, with or without a visitor’s permit).

These populations are adjusted as follows:

1. Adjustment of the population for census net undercoverage (CNU);
2. addition of independent estimates for incompletely enumerated Indian reserves in 1991, 1996, 2001 and 2006;
3. adjustment for early enumeration in 1991 and 1996 in parts of northern Quebec, Newfoundland and Labrador, the Yukon and the Northwest Territories;
4. addition of estimates of NPRs in 1971, 1976, 1981 and 1986. Since 1991, NPRs are included in the census universe;
5. estimation of the July 1 base population by addition or subtraction of the components of growth between Census Day and June 30.

Adjustment for census net undercoverage (CNU)

The adjustment for CNU is important. CNU is the difference between the number of persons who should have been enumerated but were missed (undercoverage) and the number of persons who were enumerated but should not have been or who were counted more than once (overcoverage).

Coverage studies provide undercoverage estimates for the 1991, 1996, 2001 and 2006 Censuses at the provincial and territorial levels, and for the 1971, 1976, 1981 and 1986 Censuses at the provincial level only. Estimates of overcoverage at the provincial and territorial levels are available only for the last four censuses (1991, 1996, 2001 and 2006). Overcoverage for previous censuses was estimated by assuming that the overcoverage-to-undercoverage ratio for each census between 1971 and 1986 was the same as in 1991. The CNU for the Yukon and the Northwest Territories prior to 1991 was estimated by assuming that the ratio between the CNU for each territory and the 10 provinces for each census between 1971 and 1986 was the same as in 1991.

For consistency, 1991 Census undercoverage and overcoverage were revised in 1998 to take into account the methodological improvements made in the 1996 Census coverage studies. This revision altered the CNU in all censuses between 1971 and 1986. Similarly, 1996 Census undercoverage and overcoverage were revised in 2003.

Various methods were used to produce the estimates of CNU by age and sex for 1991, 1996, 2001 and 2006. First, the national estimates of CNU based on the coverage studies by age and sex were smoothed. Then an Empirical Bayes regression model was used to generate provincial and territorial estimates of CNU by broad age groups, and a synthetic model produced estimates by single year of age. Lastly, two-way raking ⁴  was used to ensure that the CNU estimates were consistent with the provincial and territorial CNU totals and the national estimates by age and sex.

For the 1971 to 1986 period, the CNU estimates by age and sex were simply prorated to the revised CNU estimates for the total population.

B. Births and deaths

Numbers of births and deaths are derived directly from the vital statistics database of Statistics Canada’s Health Statistics Division. Although Statistics Canada manages the National system of vital statistics, the central vital statistics registries of the provinces and territories are responsible for collecting and processing the information from those administrative files. Under provincial / territorial vital statistics statutes (or similar legislation), all live births and all deaths must be registered, and all provinces and territories provide the information to Statistics Canada.

The vital statistics universe closely parallels the census universe. Both universes include births and deaths of all Canadians, immigrants and non-permanent residents (NPR) and exclude foreign residents.

Vital statistics by province or territory of residence are used to produce our final estimates of births and deaths.

When there are no vital statistics, the number of births is estimated using fertility rates by mother’s age. The number of deaths is estimated using mortality rates by age and sex. These methods are used to calculate preliminary² estimates.

Special treatment for preliminary² estimates for Quebecand British Columbia

Quebec and British Columbia provide their most recent estimates of births and deaths. The figures are used to produce preliminary² estimates. For the final estimates, the two provinces’ births and deaths are derived from the vital statistics compiled by Health Statistics Division.

If current vital statistics are unavailable for sex, the number of births by sex is derived by applying the latest birth distribution from vital statistics to the preliminary birth estimates.

If current vital statistics are unavailable by age and sex, the number of deaths by age and sex is derived by applying the mortality distribution from the last two years provided by vital statistics to the preliminary death estimates.

Levels of estimates

For information on the differences between preliminary² and final estimates, see sections B. Births and Deaths, above.

C. Immigration

Like the numbers of births and deaths, Canadian immigration statistics must be kept by law. In Canada, immigration is regulated by the Immigration and Refugee Protection Act (IRPA) of 2002. This statute superseded the Immigration Act, which was passed in 1976 and amended more than 30 times in the years thereafter. Citizenship and ImmigrationCanada (CIC) collects and processes immigrants’ administrative files. It then provides Statistics Canada with information from Field Operational Support System (FOSS) files. The information is used to estimate the number and characteristics of people granted permanent resident status by the federal government on a given date. For Demography Division, the terms immigrant and permanent resident are equivalent.

An immigrant is a person who is not a Canadian citizen by birth, but has been granted the right to live in Canada permanently by Canadian immigration authorities. The number of immigrants does not include persons born abroad to Canadian parents who are only temporarily outside the country.

Immigrants are usually counted on or after the date on which they are granted permanent resident status or the right to live in Canada.

The number of immigrants by age and sex is derived from the Field Operational Support System (FOSS).

Levels of estimates

The difference between preliminary² and final postcensal estimates lies in the timeliness of the source used to estimate this component. Since the FOSS file is continually being updated, new calculations are carried out each year to update the immigration estimates. Immigration estimates are preliminary the first year and updated the following year. They become final two years after the reference year.

D. Net non-permanent residents

Like the numbers of births and deaths, Canadian immigration statistics must be kept by law. In Canada, the non-permanent residents (NPR) are regulated by the Immigration and Refugee Protection Act (IRPA) of 2002. This statute superseded the Immigration Act, which was passed in 1976 and amended more than 30 times in the years thereafter. Citizenship and ImmigrationCanada (CIC) collects and processes the administrative files of immigrants and NPRs in Canada. It then provides Statistics Canada with information from Field Operational Support System (FOSS) files. The information is used to estimate the number and characteristics of people granted non-permanent resident status by the federal government.

Non-permanent residents (NPR) are persons who are lawfully in Canada on a temporary basis under the authority of a temporary resident permit, along with members of their family living with them. Non-permanent residents (NPR) include foreign workers, foreign students, the humanitarian population and other temporary residents. The humanitarian population includes refugee claimants and temporary residents who are allowed to remain in Canada on humanitarian grounds and are not categorized as either foreign workers or foreign students. For Demography Division, the terms non-permanent resident and temporary resident are equivalent.

Estimates of the number of NPR are based on population estimates. The number of people in CIC’s system is estimated on a specific date in each year of observation. First, the end-of-period population is estimated, and then the start-of-period population is subtracted from that estimate. That yields the net number of NPR.

Anyone who received non-permanent resident status prior to the observation date is counted. For refugee claimants, the date of their application is used. Permit holders and refugee claimants are excluded from the population if their permit has expired, if they receive permanent resident status, or if they are deported. In addition, refugee claimants are excluded if their file has been inactive for two years.

Since the FOSS file is continually being updated, the figures are recalculated for each new release period to update the estimates of the net number of NPR in Canada. Non-permanent residents (NPR) estimates are preliminary the first year and updated the following year. They are finalized two to three years after the reference year, when all other components are also final.

The net number of non-permanent residents by age and sex is derived from the Field Operational Support System (FOSS).

Levels of estimates

The difference between preliminary² and final estimates lies in the timeliness of the source used to estimate this component. Since the FOSS file is continually being updated, the figures are recalculated for each new release period to update the estimates of the net number of NPRs. Non-permanent resident (NPR) estimates are preliminary the first year and updated the following year. They become final two to three years after the reference year.

E. Emigration

The number of emigrants is estimated using data from the Office of Immigration Statistics, U.S. Department of Homeland Security, data collected by the Canada Child Tax Benefit (CCTB) program, and data from the T1 Family File (T1FF) ⁵  . The first source is used to estimate emigration to the United States. CCTB data are used to estimate emigration to other countries. The estimates of the number of child emigrants have to be adjusted because the CCTB is not universal and does not provide direct information on the number of adult emigrants. As a result, four adjustment factors are used to take into account:

1. Incomplete coverage due to a delay in the receipt and processing of the files of children eligible for the CCTB. Since it seems to take four years after the reference period for CCTB administrative files to become complete, the adjustment is made if the estimates are finalized after two years. The factor is derived from the two-year ratios of emigrant children based on two versions of the CCTB files;
2. the program’s partial coverage, that is, people who do not apply for the CCTB or are not eligible. This factor is obtained by comparing the estimated number of children in the population with the number of children in CCTB files;
3. the differential propensity to emigrate between children who are eligible for the CCTB and children who are not. This factor is obtained by comparing the emigration rates of CCTB-eligible children with the rates for all children (aged 0-17). This factor is calculated for each province and territory and is based on the last three available years of T1FF⁵;
4. the differential propensity to emigrate between adults and children. This factor generates the emigration rate for the population aged 18 and over. It is obtained by (1) calculating the average ratio over three years of the adult and child emigration rates based on T1FF⁵ data, (2) calculating the average ratio over three years of the adult and child emigration rates based on data from the Office of Immigration Statistics, U.S. Department of Homeland Security, and (3) taking the average of the two rates. This factor is calculated for Canada only.

The adult emigration rate is applied to the adult population to generate the number of adult emigrants, which is then added to the number of child emigrants to produce the number of emigrants for the entire population.

Emigration is disaggregated by province and territory based on the number of child emigrants adjusted for coverage and differential emigration.

Estimates of the number of emigrants by age and sex are obtained by disaggregating the broad age groups in the T1FF⁵ into five-year age groups based on data from the Office of Immigration Statistics, U.S. Department of Homeland Security, and disaggregating those estimates into single years of age using Sprague coefficients. The same distribution is used for all provinces and territories.

Levels of estimates

The difference between preliminary² and final estimates lies in the timeliness of the sources used to estimate this component. The same estimation method is used.

F. Net temporary emigration

Some people leave Canada to live temporarily in another country; others who were temporarily outside Canada return. The net result of those departures and returns is the component known as “net temporary emigration”. Estimates of the number of departures are derived from the Reverse Record Check (RRC), the most important census coverage study. The RRC provides an estimate of the number of people who left Canada temporarily during an intercensal period and are still out of the country at the end of the period. Estimates of the number of returns are based on two sources: the Census and Demography Division’s estimates of returning emigrants. The census provides the number of people who were outside Canada at the time of the previous census and returned during the intercensal period. That number includes all returning emigrants. Then Demography Division’s estimate of the returning emigrants’ component is subtracted to produce the number of returning temporary emigrants. The estimated numbers of departures (RRC) and returns (Census and Demography Division) yield an estimate of net temporary emigration.

That estimate is for the whole intercensal period; it is disaggregated into estimates for each of the five years in the period and then into monthly estimates using a seasonal adjustment that is an average between zero seasonality and the seasonality of emigration.

Net temporary emigration is calculated first for the national level. It is then disaggregated by province or group of provinces based on the RRC estimates of temporary emigration. For the Atlantic provinces and the territories, the estimate for the group is disaggregated on the basis of each province / territory’s proportion of the group’s total population.

Net temporary emigration can be estimated only for the intercensal period preceding the most recent census. Net temporary emigration in the current period is assumed to be the same as in the previous period for each province and territory.

The emigration age and sex distribution is applied to obtain the age and sex structure of the net temporary emigration.

Levels of estimates

The difference between preliminary² and final estimates lies in the timeliness of the emigration estimate used to calculate the seasonal adjustment for the net temporary emigration. The same estimation method is used.

G. Returning emigrants

A returning emigrant is a person who returns to Canada after having been classified as an emigrant. In a manner similar to the procedure used to calculate the number of emigrants, data from the Canada Child Tax Benefit (CCTB) file and the Canada Revenue Agency’s (CRA) ‘s T1FF⁵ are used to estimate the number of returning emigrants. Adjustment factors are applied to compensate for the fact that the CCTB program is not universal, and an adult/child ratio is used to estimate the number of adult returning emigrants. As a result, three adjustment factors are used to take into account:

1. The program’s partial coverage, that is, people who do not apply for the CCTB or are not eligible. This factor is obtained by comparing the estimated number of children in the population with the number of children in CCTB files;
2. the differential propensity to emigrate between children who are eligible for the CCTB and children who are not. This factor is obtained by comparing the emigration rates of CCTB-eligible children with the rates for all children (aged 0-17). This factor is calculated for each province and territory and is based on the last three available years of T1FFs⁵;
3. the adult / child ratio, which is based on the census used in estimating the base population.

The age and sex distribution of returning emigrants is based on Census of Canada data. Characteristics of returning emigrants are derived from census mobility data 1 year ago, after excluding non-permanent residents and immigrants. From 2006/2007, we are using distribution by age and sex derived from 2006 Census.

Levels of estimates

The difference between preliminary² and final estimates lies in the timeliness of the sources used to estimate this component. The same estimation method is used.

H. Interprovincial migration

Interprovincial migration represents movements from one province or territory to another, involving a change in usual place of residence. As is the case for emigration, there is no provision for recording interprovincial migration in Canada. Consequently, such movements have to be estimated using data from the Canada Child Tax Benefit (CCTB) of Canada Revenue Agency (CRA) and the T1FF⁵.

Final estimates of interprovincial migration are obtained by comparing addresses indicated on personal income tax returns over two consecutive tax years. However, the migration status of taxfilers’ dependants has to be imputed. An adjustment is also required to take into account migrants who do not file income tax returns. From 2001/2002 to 2005/2006, the adjustment was slightly modified (for further information, see Wilkinson, 2004). From 2006/2007, this adjustment has slightly modified (Cyr, 2008 – Internal document).

Since income tax returns are not available at the time preliminary estimates are produced, the estimation of preliminary² interprovincial migration is based on CCTB administrative files, which provide counts of child migrants (aged 0-17) receiving benefits under the program. The estimates have to be adjusted later for children who are not receiving the CCTB. Finally, the number of adult migrants is calculated using the number of child migrants and factors derived from the T1FF⁵. As a result, three adjustment factors are used to take into account:

1. The program’s partial coverage, that is, people who do not apply for the CCTB or are not receiving benefits. This factor is obtained by comparing the estimated number of children in the population with the number of children in CCTB files;
2. the differential propensity to migrate between children who are receiving the CCTB and children who are not. This factor is obtained by comparing the out-migration rates of children receiving the CCTB with the rates for all children (aged 0-17). This factor is calculated for each province and territory and is based on the last available year of T1FFs⁵;
3. the differential propensity to migrate between adults and children. This factor generates the out-migration rate of the population aged 18 and over for each province / territory of origin and destination. It is obtained by calculating the ratio of the central migration rate for adults to the rate for children. It is estimated using data from the last three available years of T1FFs⁵.

The adult migration rate is then applied to the estimated adult population. The number of adult migrants is then added to the number of child migrants to produce the number of interprovincial migrants for the entire population.

Interprovincial migration by age and sex is derived from T1FF⁵ data and counts from the last available census (1- year mobility variable). From 2006/2007, the 2006 Census age and sex distribution is used.

Levels of estimates

For information on the differences between preliminary² and final estimates of total interprovincial migration, see section H. Interprovincial migration above.

Intercensal population estimates

Intercensal estimates – population estimates for reference dates between two censuses – are produced following each census. They reconcile previous postcensal estimates with the new census counts.

There are two main steps in the production of intercensal estimates:

1. Calculation of the error of closure;
2. linear distribution of the error of closure.

Error of closure is defined as the difference between the postcensal population estimates on Census Day and the population enumerated in that census (after adjustment for census net undercoverage (CNU¹)).

The error of closure is spread uniformly over the intercensal period of days within each month.

Intercensal estimates by age and sex are adjusted in the same way, i.e., by distributing the error of closure uniformly across the age-sex cohorts.

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